Question

graph the circle. the equation of a circle is ((x - h)^2 + (y - k)^2 = r^2). center: ((-3, 2)), radius (= 3), (r^2 = 9), (r = 3)

Explanation:

Step1: Recall the circle equation

The standard form of a circle's equation is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.

Step2: Identify given values

From the notes, the center \((h, k)\) is \((-3, 2)\) and \(r^2 = 9\).

Step3: Find the radius

To find \(r\), take the square root of \(r^2\). So \(r=\sqrt{9} = 3\).

Step4: Verify the graph

The graph with center at \((-3, 2)\) (on the coordinate grid) and radius \(3\) (distance from center to circle edge) should match the red - circled graph (the middle - right graph with the red circle) as it's drawn with the correct center and radius length.

Answer:

The radius \(r = 3\), and the correct graph is the red - circled circle (the middle - right graph with the red circle) corresponding to the circle with equation \((x + 3)^2+(y - 2)^2 = 9\) (since \(h=-3,k = 2,r = 3\)).